Maths GCSE Coursework

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Maths GCSE Coursework Sample (excerpt)

Generally speaking, mathematicians can hardly be expected to take an active interest in historical research. Not only do they lack time for it, but mathematical creation is of its nature tyrannical and exclusive; it is difficult, if not impossible, for the creative mathematician to give much thought to anything else, least of all to history, which involves an intellectual effort of an absolutely different kind.

However, he may be obliged to investigate earlier writings in the very domain he is exploring, and this may lead him into historical interludes of greater or lesser frequency according to the particular constitution of his own mind. Thus a man like Klein ended in giving considerable time and thought to historical matters without ever ceasing to be a creative mathematician of the first order.

There is no doubt that a very large amount of work remains to be done, which can be done only by historically minded mathematicians rather than by mathematically minded historians. Furthermore, it is only when much of that work has been done, that is, when a great many analyses and partial syntheses of various kinds have been accomplished, that it will become at all possible to write the history of modern mathematics which Florian Cajori had in mind.

The following remarks concern chiefly the mathematician who may be induced to do from time to time some of this historical, or semi-historical, work. The purely technical difficulties on the historical side are small, incomparably smaller than in the case of ancient, mediaeval, or oriental mathematics, where they tend to predominate, but that does not mean that they do not exist. There are many pitfalls, no less dangerous because of their apparent insignificance.

The dating of discoveries is much easier, of course, than in earlier times, especially in times anterior to printing, but the dating must be more precise. Discoveries were often made almost simultaneously by different authors, and it may be necessary to determine the priority of one of them, and the dependence of the others on him, or, on the contrary, their independence from him. Controversies over priority can only be settled by very accurate dating of the rival achievements. The dates printed on books and on fascicles of periodicals may not be reliable, or if reliable, they may not be sufficiently accurate. The date of the reading of a paper before an academy or scientific society is sometimes considered as the date of publication, but this is very misleading.